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t.BA.XXM3.LA1.19HS (Linear Algebra 1)

Module: Linear Algebra 1

This information was generated on: 27 September 2021

No.

t.BA.XXM3.LA1.19HS

Title

Linear Algebra 1

Organised by

T IAMP

Credits

4

Description

Version: 3.0 start 01 August 2019

Short description

Students are familiarised with and master the basic concepts and propositions of linear algebra and analytic geometry. They can formulate simple concrete questions in the mathematical language and are able to solve these independently and present their solutions.

Module coordinator

Landry Chantal (lany)

Learning objectives (competencies)

Objectives

Competences

Taxonomy levels

You know vectors in two- and three-dimensional space and are familiar with the arithmetic operations of vector geometry.

F, M

K2, K3

You can analytically describe and solve geometric problems of the plane and the space with the help of the vector calculation.

F, M

K2, K3

You are familiar with the matrix calculus and can use it.

F, M

K2, K3

You can formulate linear systems of equations and determine, if these systems are solvable.

F, M

K2, K3

You know algorithms for solving linear systems of equations and can apply them.

F, M

K3

You master the essential properties and calculation rules of the determinants.

F, M

K2

You know algorithms for calculating determinants and can apply them.

F. M

K3

Module contents

Vector geometry:

Definition of free and bound vectors

Vector calculus in two- and three-dimensional space

Applications in analytic geometry (lines and planes)

Matrices:

Definition of a real Matrix and special square matrices

Arithmetic operations on matrices

Invertible matrix

System of linear equations:

Definition of a linear system and its representation using matrices

Solvability of a linear system and rank of a matrix

Solving a linear system: Gaussian elimination, Gauss-Jordan elimination, Cramer's rule

Applications: matrix inversion and evaluating linear independence of a set of vectors

Determinant

Definition of the determinant of a square matrix

Properties and calculation rules of the determinant

Laplace expansion for computing determinants

Applications

Teaching materials

Lecture notes, blackboard sketches, handout

Supplementary literature

Ruhrländer, M.: Lineare Algebra für Naturwissenschaftler und Ingenieure, Pearson Studium Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler (Bände I und II), Vieweg+Teubner, 12. Auflage Gramlich, G.M.: Lineare Algebra: Eine Einführung, Carl Hanser Verlag

Prerequisites

Knowledge of mathematics of the technical Berufsmatura

count only with a positive
contribution to the final
module grade with a total
of 30%

End-of-semester exam

exam

written

90 min

Grade

Min. 70%

Remarks

Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.